Finite Group Databasebeta

← #20261319

Subgroups — #20261319

Order 6208.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690804C211yesmaximal, characteristic, complemented
2#15690803C211yesmaximal, characteristic, complemented
3#15690799C211yesmaximal, characteristic, complemented
4#15690794C211yesmaximal, characteristic, complemented
5#15690792C211yesmaximal, characteristic, complemented
6#15690786C211yesmaximal, characteristic, complemented
7#15690783C211yesmaximal, characteristic, complemented
8#15690783C211yesmaximal, characteristic, complemented
9#15690782C211yesmaximal, characteristic, complemented
10#15690780C211yesmaximal, characteristic, complemented
11#15690778C211yesmaximal, characteristic, complemented
12C4×D388C211yesmaximal, characteristic, complemented
13#15690770C211yesmaximal, characteristic, complemented
14C22⋊C4×D97C211yesmaximal, characteristic, complemented
15#124×C97C211yesmaximal, characteristic, complemented
16C23×D97C2211yescharacteristic
17C2×D388C2211yescharacteristic
18C2×D388C2211yescharacteristic
19C2×C22⋊D97C2211yescharacteristic
20C2×C22⋊D97C2211yescharacteristic
21C2×C22⋊D97C2211yescharacteristic
22C2×C22⋊D97C2211yescharacteristic, complemented
23C22×Dic97C2211yescharacteristic, complemented
24C2×C4×D97C2211yescharacteristic
25C2×C4×D97C2211yescharacteristic
26C2×C4×D97C2211yescharacteristic, complemented
27C4⋊Dic97C2211yescharacteristic, complemented
28C4⋊Dic97C2211yescharacteristic, complemented
29#13095490C2211yescharacteristic, complemented
30#13095490C2211yescharacteristic, complemented
31#13095490C2211yescharacteristic, complemented
32#13095490C2211yescharacteristic, complemented
33C22⋊Dic97C2211yescharacteristic
34C22⋊Dic97C2211yescharacteristic
35#13095488C2211yescharacteristic
36#13095488C2211yescharacteristic
37#13095488C2211yescharacteristic
38#13095488C2211yescharacteristic
39#13095488C2211yescharacteristic
40#13095488C2211yescharacteristic
41#13095488C2211yescharacteristic, complemented
42#13095488C2211yescharacteristic, complemented
43C4×Dic97C2211yescharacteristic, complemented
44C2×Q8×C97C2211yescharacteristic, complemented
45C2×D4×C97C2211yescharacteristic
46C22⋊C4×C97C2211yescharacteristic
47C22⋊C4×C97C2211yescharacteristic
48C22⋊C4×C97C2211yescharacteristic, complemented
49C22⋊C4×C97C2211yescharacteristic, complemented
50C42×C97C2211yescharacteristic, complemented
51C23×C97C2311yescharacteristic
52C23×C97C2311yescharacteristic
53C22×D97—22no—
54C22×D97—41no—
55C22×D97—41no—
56C22×D97C2311yescharacteristic
57C22×D97C2311yescharacteristic
58C22×D97C2311yescharacteristic
59Q8×C97—41no—
60D4×C97—41no—
61C2×C4×C97C2311yescharacteristic
62C2×C4×C97C2311yescharacteristic
63C2×C4×C97C2311yescharacteristic
64C2×C4×C97C2311yescharacteristic
65C2×C4×C97C2311yescharacteristic
66C22⋊D97—22no—
67C22⋊D97—41no—
68C22⋊D97—41no—
69C22⋊D97—41no—
70C2×Dic97—41no—
71C2×Dic97C2311yescharacteristic
72C2×Dic97C2311yescharacteristic
73C2×Dic97C2311yescharacteristic
74C2×Dic97C2311yescharacteristic
75C2×Dic97C2311yescharacteristic
76D388—22no—
77D388—41no—
78C4×D97—41no—
79C4×D97—41no—
80C4×D97—41no—
81C22×C97—21no—
82C22×C97—21no—
83C22×C97—21no—
84C22×C97—21no—
85C22×C97—21no—
86C22×C97—21no—
87C22×C97C2411yescharacteristic
88C2×D97—21no—
89C2×D97—21no—
90C2×D97—21no—
91C2×D97—21no—
92C2×D97—21no—
93C2×D97—21no—
94C2×D97—21no—
95C2×D97—21no—
96C2×D97—44no—
97C2×D97#4112yes—
98C4×C97—21no—
99C4×C97—21no—
100C4×C97—21no—
101C4×C97—21no—
102C4×C97—21no—
103Dic97—21no—
104Dic97—21no—
105Dic97—21no—
106Dic97—21no—
107Dic97—21no—
108C2×C97—41no—
109C2×C97—41no—
110C2×C97C2×#4111yescharacteristic
111C2×C97H(5,𝔽2)11yescharacteristic
112C2×C97H(5,𝔽2)11yescharacteristic
113D97—22no—
114D97—41no—
115D97—41no—
116C97#53811yescharacteristic, complemented, Sylow
117#538—971nomaximal, Sylow
118#126—971no—
119#126—971no—
120#124—971no—
121#124D9711yescharacteristic, complemented
122#123—971no—
123#123—971no—
124C22⋊Q8—971no—
125#121—971no—
126#121—971no—
127#121—971no—
128#120—971no—
129#120—971no—
130C4×D4—971no—
131C4×D4—971no—
132C2×C22⋊C4—971no—
133C24—971no—
134C2×Q8C2×D9711yescharacteristic, complemented
135C2×D4—971no—
136C2×D4—971no—
137C2×D4—971no—
138C2×D4—971no—
139C2×D4—971no—
140C2×D4—971no—
141C2×D4C2×D9711yescharacteristic
142C22×C4—971no—
143C22×C4—971no—
144C22×C4—971no—
145C22×C4—971no—
146C4⋊C4—971no—
147C4⋊C4—971no—
148C4⋊C4—971no—
149C4⋊C4—971no—
150C4⋊C4—971no—
151C4⋊C4—971no—
152C22⋊C4—971no—
153C22⋊C4—971no—
154C22⋊C4—971no—
155C22⋊C4—971no—
156C22⋊C4—971no—
157C22⋊C4—971no—
158C22⋊C4—971no—
159C22⋊C4—971no—
160C22⋊C4—971no—
161C22⋊C4—971no—
162C22⋊C4C2×D9711yescharacteristic
163C22⋊C4C2×D9711yescharacteristic
164C22⋊C4C2×D9711yescharacteristic, complemented
165C22⋊C4C2×D9711yescharacteristic, complemented
166C42—971no—
167C42C2×D9711yescharacteristic, complemented
168C23—971no—
169C23—971no—
170C23—971no—
171C23—3881no—
172C23—3881no—
173C23—1942no—
174C23C22×D9711yescharacteristic
175C23C22×D9711yescharacteristic
176Q8—41no—
177D4—41no—
178D4—3881no—
179D4—3881no—
180D4—3881no—
181D4—3881no—
182D4—1942no—
183D4—1942no—
184C2×C4—971no—
185C2×C4—971no—
186C2×C4—971no—
187C2×C4—971no—
188C2×C4—971no—
189C2×C4—3881no—
190C2×C4—3881no—
191C2×C4—3881no—
192C2×C4—3881no—
193C2×C4C22×D9711yescharacteristic
194C2×C4C22×D9711yescharacteristic
195C2×C4C22×D9711yescharacteristic
196C2×C4C22×D9711yescharacteristic
197C2×C4C22×D9711yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—972no—
205C22—3884no—
206C22—1941no—
207C22—1941no—
208C22—1941no—
209C22—1941no—
210C22—1941no—
211C22—1941no—
212C22—1941no—
213C22—1941no—
214C22C23×D9711yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—1941no—
221C4—1941no—
222C4—1941no—
223C4—1941no—
224C4—1941no—
225C2—41no—
226C2—41no—
227C2—3881no—
228C2—3881no—
229C2—1942no—
230C2#41×D9711yescharacteristic
231C2#1569085511yescharacteristic
232C2#1569085611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D97
commutator, socleC22×C97C24
Fitting#124×C97C2
hypercenter#124D97
hypocenterC97#538
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C22 ◁ #124

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15690804C2semidirect
2. #15690803C2semidirect
3. #15690799C2semidirect
4. #15690794C2semidirect
5. #15690792C2semidirect
6. #15690786C2semidirect
7. #15690783C2semidirect
8. #15690783C2semidirect
9. #15690782C2semidirect
10. #15690780C2semidirect
11. #15690778C2semidirect
12. C4×D388C2semidirect
13. #15690770C2semidirect
14. C22⋊C4×D97C2semidirect
15. #124×C97C2semidirect
22. C2×C22⋊D97C22semidirect
23. C22×Dic97C22semidirect
26. C2×C4×D97C22semidirect
27. C4⋊Dic97C22semidirect
28. C4⋊Dic97C22semidirect
29. #13095490C22semidirect
30. #13095490C22semidirect
31. #13095490C22semidirect
32. #13095490C22semidirect
41. #13095488C22semidirect
42. #13095488C22semidirect
43. C4×Dic97C22semidirect
44. C2×Q8×C97C22semidirect
48. C22⋊C4×C97C22semidirect
49. C22⋊C4×C97C22semidirect
50. C42×C97C22semidirect
116. C97#538semidirect
121. #124D97semidirect
134. C2×Q8C2×D97semidirect
164. C22⋊C4C2×D97semidirect
165. C22⋊C4C2×D97semidirect
167. C42C2×D97semidirect